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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 174824a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 174824.b1 | 174824a1 | \([0, -1, 0, -27456, -1823636]\) | \(-235298/13\) | \(-126466775312384\) | \([]\) | \(544000\) | \(1.4638\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 174824a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 174824a do not have complex multiplication.Modular form 174824.2.a.a
sage: E.q_eigenform(10)